I have read the story, I'll try to give my opinion on the first chapter.
A boy stumbles forward through the night. His face covered in a layer of grime and clothes caked in dirt. The boy's age was still in the early years of his second decade, but he looked as if he'd been through his own fair share of struggles. Despite the rough appearance of the boy, a fierce determination to survive is found in his eyes. He trudged onward towards his destination, one hand cupped around a bundle of cloth.
What template you wrote the story in? Present tense or Past tense? While mixing between was fine, but people much preferable one style, either Present or Past...
Hmm... What's the characteristic of the boy? You have to give visualization to the reader even only a hair color or his cloth or something, you can also twine it like this, 'His face covered in a layer of grime, not that add anything to his already unseemingly face (not handsome, crude, or whatever you wish to say).
You can also simplify the paragraph, 'The moon dimly shone, a boy covered in grime and dirt stumbled toward his destination, he heaved as a bundle of cloth within his grasp, he was young, probably in the early of the second decade, but his eyes told an intense will to live.'
The boy finally stops as he reaches a stack of cardboard boxes. To the common eye, the boxes looked like nothing but a pile of rubbish built up over the years, but to the boy, it was home. Finally making it back to his squalid shelter, the boy felt ready to collapse. However, he stopped himself.
In front of him was a stack of cardboard, a pile of rubbish he had built over the years, he reached out his hand and readied to collapse inside.
That line above was enough to tell the reader it was the boy's home, the sentiment and everything also had been conveyed.
Maybe consider comma instead? It's more appropriate, or you can also use '...'
"Please... leave me alone." The voice cried. A pleading look in the figure's eyes as they were on the verge of crying.
The voice... cried?
Maybe 'the figure said, eyes full of pleading as if they were on the verge of crying.'
The boy, almost compelled to leave at that very moment, renewed his determination and approached the figure once again. The figure cried out once again but the boy paid it no mind as he reached forward to grip the figure by the arm. His hands wrapped around the figure and he pulled as if dragging an intruder out of his home. Which was exactly what he was doing.
"I don't care who you are, but this is my home, and… and you don't belong here."
His tug at the figure was met with no resistance as it was pulled out from the makeshift cardboard shack and onto the dirty alleyway. The figure now out of the shadows of the shelter was illuminated by the faint moonlight.
"Please, please, I don't want to go back..." She cried, her voice began to falter.
A young girl, no older than himself, covered in cuts and bruises. The boy may have been covered in dirt and grime, but he was still uninjured. The girl, however, was relatively clean. Almost as if she had taken a bath earlier in the day. But the wounds, the cuts and the bruises, they looked worse than anything the boy had ever experienced.
Despite the injuries, she didn't cry out in pain from being dragged away from the cardboard shelter. Her two grey-white eyes just stared at the boy, as if pleading for mercy. The boy attempted to put on a tough front.
People intuitively resist if they were forcefully being pulled, and the dialogue suggested she was resisting... the proper dialogue if she's not resisting was something like, 'I am sorry... I am sorry... I have nowhere to go...'
The boy lay on his side as if to block the image of her out of his sight and mind. However, his mind was cruel and was filled with nothing but curiosity towards the young girl.
The boy laid in the opposite direction from the girl, his mind, however, constantly providing curiosity toward her.
Again, simplicity...
The boy sat up, and violently scratched at his head.
You don't need 'at'
Well, all in all, the story is great, I am curious whether you will make the story following their age till they grow up, or you will do time skip? like these two chapters were just prologue, and the real story began when the pair was in their 20s or something...